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The expression for the average number of people (8x³ +70x² +145x+182)/(2x + 13)

From the question, we have the following parameters that can be used in our computation:

The total number of people, f(x) = 8x³ +70x² +145x+182

Number of free books = 2x + 13

To determine the average number of people that download each of the free books,

We need to divide the total number of people that register by the number of free books available.

So, we have

Expression = (8x³ +70x² +145x+182)/(2x + 13)

Hence, the expression is (8x³ +70x² +145x+182)/(2x + 13)

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1. The height of the cone is, 22.18 mm.

2. The slant height is, 28.14 mm.

3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

The volume of cone V = (1/3)πr²h

Given that,

The volume  = 8792 mm³

1. by using the formula to solve for h,

we get h = (3V)/(πr²).

Plugging in the values given,

we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.

Therefore, the height of the cone is approximately 22.18 mm.

2. it is known that, from the Pythagoras theorem

s² = h² + r²,

where s is the slant height, h is the height, and r is the radius.

Plugging in the values we found in part 1,

we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².

Taking the square root of both sides, we get s ≈ 28.14 mm.

Therefore, the slant height is approximately 28.14 mm.

3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.

Using the value we found in part 2,

the length of the slant height is approximately 28.14 mm.

Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.

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The value of summation of ( x-2)² is 973

A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.

if

x (x-2) ( x-2)²

15 13 169

13 11 121

13 11 121

4 2 4

19 17 289

12 10 100

6 4 16

5 3 9

14 12 144

Therefore the summation of (x-2)²

= 169+121+121+4+289+100+16+9+144 = 973

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Answer:answer

Step-by-step explanation:

The value of summation of ( x-2)² is 973

The area of the given composite figure with a side length of 14mm and an edge length of 8mm is 158.2 mm².

What is a composite figure?

A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. A variety of forms that we encounter every day are composite figures that can be created from two or more fundamental figures.

The figure is given below.

From the figure, we can see that the sides of a triangle at the top and bottom are the same.

So the triangle cut from the bottom is placed at the top of the figure.

When the cut triangle is placed back at the bottom, we get a rectangle of length 14 mm and breadth 11.3 mm, as given below.

So the area of the given composite figure is the same as the area of the rectangle.

The area of the rectangle = length * breadth = 14 * 11.3 = 158.2 mm²

Therefore the area of the given composite figure is 158.2 mm².

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y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y=x+0.6

Find the y value for x=3, 4.2, 2

When x=3

y=3+0.6=3.6

When x=4.2

y=4.2+0.6=4.8

When x=2

y=2+0.6=2.6

Therefore, y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

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A quotation isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2.

The option (a) is correct.

Famous people who discuss their opinions on a given subject often employ quotation marks around their words. The brief nature of a quotation allows it to share individuality. The citation served as a means of sharing ideas and serving as a source of historical information.

The quotation, which is sometimes referred to as "quote vomit," was cut off from the remainder of the text.

The sentences are directed at their objective. Understanding how the universe functions and how we fit into it can be done through the metaphor of weaving.

As a result, the quote isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2. Therefore, option (a) is correct.

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Answer:

There are 12 desktop computers and 20 laptop computers.

Step-by-step explanation:

32:2=16

8:2=4

16-4=12

16+4=20

The ratio 8.64 : 37.76 as a fraction will be 27/118.

What precisely is ratio?

Ratios and proportions are typically described using fractions. When a fraction is presented as a:b, a ratio is shown, whereas a percentage suggests that two ratios are equal. In this case, a and b can be any two numbers. The ratio and proportion are two essential notions that serve as a foundation for understanding other concepts in mathematics and science.

In our daily lives, we apply the notion of ratio and proportion, such as in business when dealing with money or in cooking.

As a consequence, when b is greater than zero, the ratio specifies the connection between two variables, such as a:b. The 2:4 ratio, for example, is written as 2:4 = 1:2. 

Now,

Given ratio is  8.64 : 37.76

we can write this as 8.64/37.76

=864/3776

=432/1888

=216/944

=54/236

=27/118

Hence,

             The ratio 8.64 : 37.76, as a fraction will be 27/118.

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Answer:

Shortage

Step-by-step explanation:

If the market price of a product is set below the equilibrium price, it will create a shortage of the product because the demand exceeds the supply.

a. Yes, The answer is correct.

b. When we subtract the second equation from the first, the next step would be 3x = 9.

What is a system of linear equations?

The collection of two or more linear equations involving the same variables is known as a system of linear equations. In this case, linear equations are first-order equations, where the maximum power of the variable is 1.

Part a:

Given that, a customer purchases 8 bags of cat food and 2 bags of dog food, then the total weight of the purchase is 44 pounds.

Another customer purchases 5 bags of cat food and 2 bags of dog food, then the total weight of the purchase is 35 pounds.

let the weight of the cat food be 'x' and the dog food is 'y'.

For the first customer,

Total weight will be = 8x + 2y = 44 .....eq 1

For the second customer,

Total weight will be = 5x + 2y = 35 .....eq 2

Which are the two equations given above,

So, The equations are correct.

Part b:

Eliminate y terms from the equations.

Subtract eq 2 from eq 1:

 8x + 2y = 44

-(5x + 2y = 35)

______

 3x + 0  = 9

3x = 9, which contradicts the above-given step '13x = 79'

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The inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

f ( x ) = ( 5/x ) + 4   be equation (1)

On simplifying the equation , we get

y = ( 5/x ) + 4

Now , replacing x with y , we get

x = ( 5/y ) + 4

On solving for y , we get

5/y = x - 4

y = ( 5 / x - 4 )

Now , the inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )

Hence , the equation is f⁻¹ ( x ) = 5 / ( x - 4 )

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The answers include the following:

This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.

From the graph, we can deduce that Runner A won the race because it attained a greater distance when compared to the time for all the other runners.

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Answer:

{30.1,30.7}

Step-by-step explanation:

[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{90\%}=30.4\pm1.645\biggr(\frac{5.5}{\sqrt{686}}\biggr)\\\\CI_{90\%}\approx30.4\pm 0.3\\\\CI_{90\%}=\{30.1,30.7\}[/tex]

Thus, we are 90% confident that the true amount of mmHg that is lowered will be between 30.1 and 30.7 mmHg.

7.21 × 10⁻⁷

Step-by-step explanation:

(6.94 × 10⁻⁷) + (2.7 × 10⁻⁸) = 7.21 × 10⁻⁷

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Answer:

x = -5

Step-by-step explanation:

15 - 2x = -4(x+1) + 9

-4(x+1) can be distributed and simplified to -4x - 4

15 - 2x = -4x - 4 + 9

15 - 2x = -4x +5

-2x + 4x = 5 - 15

2x = -10

x = -5

Answer:

[tex]x=-5[/tex]

Step-by-step explanation:

Given

[tex]15-2x=-4(x+1)+9[/tex]

Simplify the right side by applying the distributive property.

[tex]15-2x=(-4*x)+(-4*1)+9[/tex]

[tex]15-2x=-4x-4+9[/tex]

Add [tex]-4[/tex] and 9.

[tex]15-2x=-4x+5[/tex]

Add [tex]4x[/tex] to both sides of the equation.

[tex]15-2x+4x=5[/tex]

Add [tex]-2x[/tex] and [tex]4x[/tex].

[tex]15+2x=5[/tex]

Subtract [tex]15[/tex] from both sides of the equation.

[tex]2x=-10[/tex]

Divide both sides of the equation by [tex]2[/tex].

[tex]x=-5[/tex]

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The two integers that are between -83 and +83 are -82 and +82.

What is integers ?

In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.

There are multiple pairs of integers that are between -83 and 83.

Here are two examples:

-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -50 0 50 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -75 0 75 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.

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Answer:

Step-by-step explanation:

Calculated based on 2 given angles and 1 given side.

∠B = 180° - A - C = 0.99484 rad = 57°

∠B = 57°

a = c·sin(A)/sin(C) = 527.21059

b = c·sin(B)/sin(C) = 811.83311

Answer:

qr rs st qt are the line hope it helped

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]

The elements of the set A are given as follows:

A = {January, February, March, April, May, June, July, August, September, October, November, December}.

The set A in the context of this problem is defined as follows:

A = {x | x is a month of the year.}

Hence the set A is composed by 12 elements, which are all the months of an year, as follows:

A = {January, February, March, April, May, June, July, August, September, October, November, December}.

The problem asks for all the elements of the set A, given as follows:

A = {x | x is a month of the year.}

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Answer: The range of the tangent function is (-∞,∞). So the answer is A: All real numbers.

Step-by-step explanation:

So here we have a hole in a steel plate with a diameter of 1.166 cm. So we need to find the temperature at what temperature is the diameter of full equal to 1.165 cm. So you're given is D. I. That is equal to initial diameter. That is equal to 1.166 cm. and temporary Germany shirt temperature is equal to 23°C and DF is equal to 1.165 m. This is the final diameter. So you only need to find the value of P. F. So we know that whole diameter very nice linearly with And nature. So here we can say DFS equal to D. I multiplied by one plus alpha. They're dirty. Yeah, I'll find that coefficient of thermal expansion. So here we can say it this is for steel And the value of alpha is equal to 13, multiplied by 10, raised to -6. So D F. Is equal to B. I multiplied plus the I'm multiplied by alpha, multiplied by delta T. So here we can see it D F minus D. I. That is the initial final diameter minus initial diameter divided by D. I. Alpha. That is equal to delta P. So this will be where to tell 30. That is equal to -6.59717. multiplied by 10° to -5 divided by And there's do -6. So here the key Is equal to -65.9717 degree. So here P f minus T I is equal to minus 65.9717 degree. The T.F will be equal to 23 -65.9717. So therefore final temperature that this T.F is equal to -42.8717 degrees Celsius. So therefore this is the answer to the question. So here we can say hands, final temperature Is equal to -42.8717°C.

Answer:

= 7022cm

Step-by-step explanation:

The Perimeter of a rectangle =

[tex] = 2(l) + 2(w)[/tex]

From the question

L= 15.47m

w= 19.64m

therefore perimeter of a rectangle

=

[tex] = 2(15.47) + 2(19.64) \\ = 30.94 + 39.28 \\ = 70.22 m[/tex]

Also since rectangle are in centimetres

than if. 1 m = 100cm

than 70.22m = ?

therefore 70.22/1 = 100cm

=7022cm

therefore the Perimeter of a rectangle = 7022

The distance from point A to point B measures is 1,269.9 feet.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

Given;

The horizontal distance= 1196ft

Angle of elevation to the lighthouse’s=13°

Angle of elevation from point B =3 °

Now,

Distance from A to B = D;

D = Horizontal distance from B to LH - Horizontal distance from A to LH

Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet;

Therefore, by the trigonometric ratios the distance from point A to point B, D will be 1,269.9feet;

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By using the composition of functions, we can find valid decompositions of c(x) using f(x) = [tex](x+1)^{1/3}.[/tex] and g(x) = x²

A function is a rule that takes an input value and produces an output value.

One way to do this is to use the composition of functions. The composition of two functions f(x) and g(x) is denoted as f(g(x)). This means that we first apply g(x) to the input, and then apply f(x) to the output of g(x). In other words, we first evaluate g(x), and then plug that result into f(x) to get the final output.

Using this concept, let's look at the first set of functions. We are given

=> c(x) = f ◦ g (x) = (x²) f(x) = [tex](x+1)^{1/3}.[/tex]

This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x², and f(x) = [tex](x+1)^{1/3}.[/tex] This is a valid decomposition of c(x).

Similarly, in the second set of functions, we have

=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x² + 1.

This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x² + 1, and [tex](x+1)^{1/3}.[/tex] This is also a valid decomposition of c(x).

In the third set of functions, we have

=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x + 1, and f(x) = [tex](x^2)^{1/3}=x^{2/3}[/tex]

This is another valid decomposition of c(x).

Finally, in the fourth set of functions, we have

=> c(x) = f ◦ g (x) = x² g(x) = [tex](x+1)^{1/3}[/tex], and f(x) = [tex]x^{2/3}[/tex].

This is yet another valid decomposition of c(x).

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The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.

Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³

The volume of this cylinder is 1.5 times that of the cone

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The probability that the sample proportion is less than 0.33 is approximately 0.7422.

The sample proportion of first-time customers can be modeled by a normal distribution with mean p, the true proportion of first-time customers, and standard deviation [tex]\sqrt{\frac{p(1-p)}{n}}[/tex], where n is the sample size.

In this case, p = 0.32, n = 80, and we want to find [tex]P(\hat{p} < 0.33)[/tex].

The standardized version of [tex]\hat{p}[/tex] is given by:

[tex]z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

Substituting the values, we get:

[tex]z = \frac{0.33-0.32}{\sqrt{\frac{0.32(1-0.32)}{80}}} \approx 0.6579[/tex]

Using a standard normal distribution table (or a calculator or statistical software), we find that the probability of z being less than 0.6579 is approximately 0.7422.

Therefore, the probability that the sample proportion is less than 0.33 is approximately 0.7422.

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The given differential equation:

y''' − 2y'' + y' = 2 − 24ex + 40e5x,

y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2

Therefore, the next solution is 13/2

Differential Equation:

In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.

Now,

Given differential equation is

y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ                 ------------ (1)

Auxiliary equation is m³ - 2m² +2m = 0

Now,

   m(m² - 2m +2) = 0

⇒ m(m-1)² = 0

Therefore, m = 0,1,1

Therefore,

[tex]y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}[/tex]

Now, we have to find the particular solution by method of undetermined coefficient.

   [tex]y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}[/tex]

⇒ [tex]y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}[/tex]

⇒ [tex]y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}[/tex]

⇒ [tex]y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}[/tex]

Putting these values in differential equation (1), we get:

y'''(0) = 13/2

Complete Question:

Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2

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The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.

In financial accounting, a cash flow statement, often called a statement of cash flows, is a financial statement that breaks down the analysis into operating, investing, and financing operations. It illustrates how changes in balance sheet accounts and income effect cash and cash equivalents.

A cash flow statement lists all of an organization's cash inflows from current operations and outside investment sources. The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.

Functionally speaking, cash flows are categorized according to the nature of the underlying transaction. The statement's main goal is to give pertinent details about the agency's cash inflows and outflows during a given time period.

Therefore, the correct answer is option d) Determine the change in cash.

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